What are the prohibitions and obligations upon a woman during her iddah (waiting period), and is it permissible to recite Al-Fatihah or speak to her about engagement during the iddah?

The waiting period (iddah) for widowhood or an irrevocable divorce: It is not permissible to explicitly propose marriage to a woman observing this waiting period, but it is permissible to make an indirect hint.

The waiting period (iddah) for a revocable divorce: It is impermissible, by consensus, to either explicitly propose or indirectly hint at marriage to a woman observing this waiting period.